The generator matrix

 1  0  1  1  1  0  1  1  X  1  1  X  1  1  0  1  1  0  1  1  X  1  1  X  1  1  1  1  1  1  1  1  0  0  X  X  X  X  0  0  1  1  1  1  0  X  1  1  X  X  0  1  1  0  X  X  X  0  0  X  X  0  1  1  0  1  1
 0  1  1  0 X+1  1  X X+1  1  X  1  1  0 X+1  1  0 X+1  1  X  1  1  X  1  1  0  0 X+1 X+1  X  X  1  1  1  1  1  1  0  X  X  0  0  X X+1  1  1  1  0  X  0  X  X X+1  1  1  1  0  X  X  0  0  X  X  0 X+1  1  X  0
 0  0  X  X  0  X  X  X  X  0  0  0  0  0  X  X  X  0  X  X  X  0  0  0  0  X  0  X  X  0  X  0  0  X  X  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  0  0  X  X  X  X  0  0  0  0  0  X  0  X

generates a code of length 67 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+16x^68+12x^70+3x^72

The gray image is a linear code over GF(2) with n=134, k=5 and d=68.
As d=68 is an upper bound for linear (134,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0675 seconds.